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Evaluate:

\(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + \sqrt{49}}}}}\)

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RPF Constable 2024 Official Paper (Held On 03 Mar, 2025 Shift 2)
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  1. 7
  2. 5
  3. 6
  4. 9

Answer (Detailed Solution Below)

Option 1 : 7
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Detailed Solution

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Expression: \(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + \sqrt{49}}}}}\)

Calculation:

\(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + \sqrt{49}}}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + 7}}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{49}}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{74 + 7}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{81}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + 9}}\)

⇒ \(\sqrt{42 + \sqrt{49}}\)

⇒ \(\sqrt{42 + 7}\)

⇒ \(\sqrt{49} = 7\)

The value of the expression is 7.

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